Imagine you have to design an air-spaced doublet lens, and because of the cost restrictions placed on the final system you have a  good feel for what the manufacturing tolerances will have to be. Here is the traditional design process.

Note: all files referred to in this article are included in the zip archive that can be downloaded from the last page of this article. The file TOLR999.TOP must be placed in your root /zemax folder, the other files can be placed wherever you want.

Open the sample file Doublet_Starting_Point.zmx. This shows a rough starting point for our design, which is an air-spaced doublet operating over a small field of view and across the visible wavelength spectrum. A default merit function, which minimizes the RMS spot across both field and wavelength, and which contains useful boundary conditions on the thickness ranges of both glass and air surfaces, has already been built. Optimize the lens, and you should get the following result:

The RMS spot size over field looks very good:



However we must now tolerance the lens to see what we can expect to get in production. A set of (rather loose) tolerances has already been built, and a compensator has been set on the back focal distance so that some refocus is attempted. Remove all the variables and the f/# solve on the last surface. Run the tolerancer by clicking on Tools ... Tolerancing ... Tolerancing. Press the Load button:



and navigate to the file TOLR999.TOP. This will configure the tolerancer as follows:



The Monte Carlo runs show a dramatic reduction in performance:



with these statistics:





The sensitivity analysis, which takes each tolerance individually, shows:



and it can be seen that the expected performance is ten times worse than the nominal performance. This means our design is far too delicate for the manufacturing tolerances we are going to use.